Escher's most mathematically interesting piece

Escher's Print Gallery, and the tour of complex analysis it invites.
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Original paper by de Smit and Lenstra:
https://pub.math.leidenuniv.nl/~smitbde/papers/2003-de_smit-lenstra-escher.pdf

Timestamps:

0:00 - The print gallery
13:04 - Conformal maps from complex analysis
21:41 - The complex exponential
25:56 - The complex logarithm
32:32 - 3b1b Talent
33:14 - Constructing the key function
40:16 - The deeper math behind Escher

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These animations are largely made using a custom Python library, manim. See the FAQ comments here:
https://3b1b.co/faq#manim

Music by Vincent Rubinetti.
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

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